In this research, fully degradable elastomeric sealing materials were developed to enhance the environmental sustainability of oil and gas extraction. The modification of millable polyurethane rubber (MPU) with polyglycolic acid/hydrogenated nitrile butadiene rubber (PGA/HNBR) led to the synthesis of PGA@MPU/HNBR composite materials. The impact of varying monomer quantities on the mechanical properties, degradation behavior, degradation mechanisms, and thermal stability of these materials was investigated. Our findings illustrate that an increasing proportion of HNBR in the PGA@MPU/HNBR composite materials resulted in a decreased degradation rate. Simultaneously, higher HNBR content improved the thermal stability of the materials, while the inclusion of PGA reduced material hardness, rendering the composites more susceptible to swelling. At an HNBR content of 40 phr, MPU at 60 phr, and PGA at 6 phr, the composite material demonstrated the highest retention of mechanical properties at 31.3% following 168 h of hydrolysis at 100 °C. The degradation of the composite materials in 100 °C water primarily resulted from the hydrolysis of MPU’s ester groups, with HNBR remaining unaffected.